Field of the Invention
Due to the fact that the integration density of electrical circuits is becoming ever greater (VLSI), it is becoming more and more complex to determine system states of an electrical circuit, for example by means of a circuit simulation. The integration densities attained in modern circuits are already so great that even parasitic effects, for example crosstalk effects between lines which connect the individual components of the electrical circuit to one another, must be considered. The lines are normally modeled as linear components, for example as a sequence of RC elements. If the integration density is high, the additional modeling of lines leads to an increased number of sets of mutually coupled linear components within an electrical circuit, which are in each case coupled to non-linear components of the electrical circuit. Expressed figuratively, this results in "islands" of mutually coupled linear components of an electrical circuit that is to be investigated.
The large number of coupled linear components which are caused, for example, by modeling the parasitic effects in the lines subject the computers that are used in the investigation of the individual electrical circuits to requirements which cannot be satisfied at the moment, even by very high-performance computers.
A so-called eigenvalue solver for determining eigenvalues for a homogeneous differential equation system is known from Booten et al., "A Preconditioned Jacobi-Davidson Method for Solving Large Generalized Eigenvalue Problems," Report NM-R9414, Centrum voor Wiskunde en Informatica, Netherlands, ISSN-0169-0388 (1994).
The determination of a transfer function for a set of coupled linear components is described in Vlach and Singhal, "Computer Methods for Circuit Analysis and Design," Van Nostrand Reinhold Company, New York, ISBN-0-442-28108-0 (1983).
A process is known for the approximation of a transfer function for a set of coupled linear components of an electrical circuit, in which only the so-called dominant eigenvalue is considered. See Glashoff and Merten, "Neue Verfahren zur Laufzeitberechnung bei Semi-Custom-Schaltungen," [New Methods for Delay Time Calculation in Semi-Custom Circuits]; Informatik in der Praxis, Springer, ISBN 3-540-17054-5, p. 13-26 (1986).
A plurality of transfer functions can be determined separately for a set of linear components. The transfer functions thus each describe the response of the set of linear components with respect to two reference connections for the respective transfer function. This is described by Ratzlaff and Pillage, "RICE: Rapid Interconnect Circuit Evaluation Using AWE," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 13, No. 6, pp. 763-76, June 1994.
The method described by Vlach and Singhal has the disadvantage that, there, only the state of the set of linear components is considered, and only with respect to two connections of the set of linear components to non-linear components. It is not possible to use that method to consider a greater number of connections to further non-linear components.
The method described by Ratzlaff and Pillage has the disadvantage, inter alia, that, although a number of connections of the set of linear components to linear components are considered, these are, however, in each case always only in pairs. On the one hand, therefore, this requires increased computation capacity for carrying out the method and, on the other hand, the accuracy of the results which are achieved by that method is very low.